Unit 6 : Thermodynamics
6.6.1. Second Law of Thermodynamics
6.8. Third Law of Thermodynamics

Unit 7 : Equilibrium

7.12.1 pH of Buffer Solutions

Class XII
Unit 16 :

Chemistry in Everyday Life

16.4.2.1

Antioxidants
3

Unit 5: States of Matter
5.7.1 KINETIC ENERGY AND MOLECULAR SPEEDSAs you have studied in the previous section the molecules of a gas are always in motion and are colliding with each other and with the walls of the container. Due to these collisions the speeds and the kinetic energies of the individual molecules keep on changing. However at a given temperature, the average kinetic energy of the gas molecules remains constant.

If at a given temperature, n1 molecules have speed v1, n2 molecules have speed v2, n3 molecules have speed v3, and so on. Then, the total kinetic energy (EK) of the gas at this temperature is given by

where m is the mass of the molecule.
The corresponding average kinetic energy (

If the following term

Then the average kinetic energy is given by

where c is given by

4

) of the gas will be

This ‘c’ is known as root-mean-square speed. As the name implies, to calculate c, first take the squares of the individual speeds, then their mean and finally the square root of the mean.
It can be shown that c is related to temperature by

The average kinetic energy depends only on absolute temperature and is related to absolute temperature by the expression

where k = Boltzmann constant = 1.38 x 10-23 J K-1
In the case of gases, one also talks of two other speeds, namely, average speed and most-probable speed.
The average speed ( ) at a given temperature is the arithmetic mean of the speeds of different molecules of the gas. i.e,

where n1 molecules have speed v1, n2 molecules have speed v2, n3 molecules have speed v3, and so on.
The relationship between average speed and temperature T is given by

The most probable speed ( ) of a gas at a given temperature is the speed possessed by the maximum number of molecules at that temperature. Unlike average speed and root mean square speed, the most probable speed cannot be expressed in terms of the individual molecular speeds.

The most probable speed (

) is related to absolute temperature (T) by the expression

5

Relationship between different types of molecular speeds
The three types of molecular speeds, namely, most probable speed ( ), average speed ( ) and root mean square speed (c) of a gas at a given temperature are related to each other as follows:

For a particular gas, at a particular temperature,

It follows from the above relationships that

Example:
Calculate the root mean square, average and most probable speeds of oxygen molecules at 27 oC.

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